The efficiency for converting baryonic gas into stars,
which can be characterized by \(M_{\rm c}/M_{\rm h}\) ,
peaks at a mass \(\log (M_{\rm h, p}/\, h^{-1}{\rm M_\odot })\sim 12\) .
[1]} found that the quenched fraction for centrals
increases with \(M_{\rm h}\)  very quickly around \(M_{\rm h, p}\) .
These results imply that a large
fraction of central galaxies have their star formation
quenched when their halos reach \(M_{\rm h, p}\) 
[2]}, [3]}.
Interestingly, halos of \(10^{12}\, h^{-1}{\rm M_\odot }\)  are also important for AGN activities, as shown in Section 
[4]}, [5]}.
One scenario proposed in the literature
is that AGN feedback can quench the star formation
in their host galaxies. This is supported by the
high AGN fraction at \(D_n4000=1.5\sim 1.6\) 
(Figure REF ), where the transition
from star-forming to quiescent population occurs.
Since the timescales for AGN activities and
quenching are expected to be shorter
than that for halo growth, one would expect
that AGNs have the same SHMR as star-forming galaxies,
consistent with our results in Figure REF .
However, there are unresolved problems in
this scenario. In the local Universe, AGN radiation
and their winds are usually weak [6]},
and it may be difficult to expel cold gas from host galaxies.
Moreover, the timescale for galaxy
quenching is about 1 Gyr, while the timescale for
one cycle of AGN activity is much smaller.
Thus, the observed AGNs are unlikely the ones
that expelled the cold gas and quenched the star formation.
